#include "sofa.h"

double iauEors(double rnpb[3][3], double s)
/*
**  - - - - - - - -
**   i a u E o r s
**  - - - - - - - -
**
**  Equation of the origins, given the classical NPB matrix and the
**  quantity s.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards Of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     rnpb  double[3][3]  classical nutation x precession x bias matrix
**     s     double        the quantity s (the CIO locator) in radians
**
**  Returned (function value):
**           double        the equation of the origins in radians
**
**  Notes:
**
**  1)  The equation of the origins is the distance between the true
**      equinox and the celestial intermediate origin and, equivalently,
**      the difference between Earth rotation angle and Greenwich
**      apparent sidereal time (ERA-GST).  It comprises the precession
**      (since J2000.0) in right ascension plus the equation of the
**      equinoxes (including the small correction terms).
**
**  2)  The algorithm is from Wallace & Capitaine (2006).
**
** References:
**
**     Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
**     Wallace, P. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
**  This revision:  2021 May 11
**
**  SOFA release 2021-05-12
**
**  Copyright (C) 2021 IAU SOFA Board.  See notes at end.
*/
{
   double x, ax, xs, ys, zs, p, q, eo;


/* Evaluate Wallace & Capitaine (2006) expression (16). */
   x = rnpb[2][0];
   ax = x / (1.0 + rnpb[2][2]);
   xs = 1.0 - ax * x;
   ys = -ax * rnpb[2][1];
   zs = -x;
   p = rnpb[0][0] * xs + rnpb[0][1] * ys + rnpb[0][2] * zs;
   q = rnpb[1][0] * xs + rnpb[1][1] * ys + rnpb[1][2] * zs;
   eo = ((p != 0) || (q != 0)) ? s - atan2(q, p) : s;

   return eo;

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2021
**  Standards Of Fundamental Astronomy Board
**  of the International Astronomical Union.
**
**  =====================
**  SOFA Software License
**  =====================
**
**  NOTICE TO USER:
**
**  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
**  CONDITIONS WHICH APPLY TO ITS USE.
**
**  1. The Software is owned by the IAU SOFA Board ("SOFA").
**
**  2. Permission is granted to anyone to use the SOFA software for any
**     purpose, including commercial applications, free of charge and
**     without payment of royalties, subject to the conditions and
**     restrictions listed below.
**
**  3. You (the user) may copy and distribute SOFA source code to others,
**     and use and adapt its code and algorithms in your own software,
**     on a world-wide, royalty-free basis.  That portion of your
**     distribution that does not consist of intact and unchanged copies
**     of SOFA source code files is a "derived work" that must comply
**     with the following requirements:
**
**     a) Your work shall be marked or carry a statement that it
**        (i) uses routines and computations derived by you from
**        software provided by SOFA under license to you; and
**        (ii) does not itself constitute software provided by and/or
**        endorsed by SOFA.
**
**     b) The source code of your derived work must contain descriptions
**        of how the derived work is based upon, contains and/or differs
**        from the original SOFA software.
**
**     c) The names of all routines in your derived work shall not
**        include the prefix "iau" or "sofa" or trivial modifications
**        thereof such as changes of case.
**
**     d) The origin of the SOFA components of your derived work must
**        not be misrepresented;  you must not claim that you wrote the
**        original software, nor file a patent application for SOFA
**        software or algorithms embedded in the SOFA software.
**
**     e) These requirements must be reproduced intact in any source
**        distribution and shall apply to anyone to whom you have
**        granted a further right to modify the source code of your
**        derived work.
**
**     Note that, as originally distributed, the SOFA software is
**     intended to be a definitive implementation of the IAU standards,
**     and consequently third-party modifications are discouraged.  All
**     variations, no matter how minor, must be explicitly marked as
**     such, as explained above.
**
**  4. You shall not cause the SOFA software to be brought into
**     disrepute, either by misuse, or use for inappropriate tasks, or
**     by inappropriate modification.
**
**  5. The SOFA software is provided "as is" and SOFA makes no warranty
**     as to its use or performance.   SOFA does not and cannot warrant
**     the performance or results which the user may obtain by using the
**     SOFA software.  SOFA makes no warranties, express or implied, as
**     to non-infringement of third party rights, merchantability, or
**     fitness for any particular purpose.  In no event will SOFA be
**     liable to the user for any consequential, incidental, or special
**     damages, including any lost profits or lost savings, even if a
**     SOFA representative has been advised of such damages, or for any
**     claim by any third party.
**
**  6. The provision of any version of the SOFA software under the terms
**     and conditions specified herein does not imply that future
**     versions will also be made available under the same terms and
**     conditions.
*
**  In any published work or commercial product which uses the SOFA
**  software directly, acknowledgement (see www.iausofa.org) is
**  appreciated.
**
**  Correspondence concerning SOFA software should be addressed as
**  follows:
**
**      By email:  sofa@ukho.gov.uk
**      By post:   IAU SOFA Center
**                 HM Nautical Almanac Office
**                 UK Hydrographic Office
**                 Admiralty Way, Taunton
**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/
}
